A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves

2022/05/12 by Shijie Shang, Shang, Shijie
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2205.06289

openalex publication_date 2022/05/12 · openalex created_date 2022/11/03 · openalex updated_date 2026/07/28

Abstract

We show that a bound of the Castelnuovo-Mumford regularity of any power of the ideal sheaf of a smooth projective complex variety X⊆ℙ^r is sharp exactly for complete intersections, provided the variety X is cut out scheme-theoretically by several hypersurfaces in ℙ^r. This generalizes a result of Bertram-Ein-Lazarsfeld.

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